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Question

A heavy uniform chain lies on a horizontal tabletop. If the coefficient of friction between the chain and the table surface is0.25, then the maximum fraction of the length of the chain that can hang over one edge of the table is


A

20%

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B

25%

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C

35%

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D

15%

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Solution

The correct option is A

20%


Step 1. Given data

The coefficient of friction between the chain and the table surface is0.25.

Step 2. Formula used

fmax=μN

Where μ is the coefficient of friction and N is the normal force.

Step 3. Explanation for correct option

Let x be the length of the chain on the table and L-x is the length hanging.

Let the total mass is M.

Therefore the mass of the chain hanging is ML-xL.

Mass of the chain on the table MxL.

fmax=μN=μMgxL where g is the acceleration due to gravity.

Weight of the chain hanging,

W=m'g=ML-xgL

For the system to be stable

ML-xgL=μMgxLL-x=0.25xx=45L

Therefore the hanging part is L-x=L-4L5=L5

Now we calculate the percentage:

L5L×100=20%

Hence, the correct option is option A.


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